I'm a little confused about the analysis of normality in a repeated measures ANOVA I'm doing. It's a factorial ANOVA with three rm IVs each of which has only 2 levels. I've read in a few places online and in a book or two that to assess normality in a repeated measures ANOVA, I look at the distributions within each conditions -this would be 8 distributions in my case. However, most of these articles focused on rm ANOVAs in which at least one of the IVs has more than 2 levels.
My confusion is coming from the fact that when carrying out a repeated measures t test (i.e. 1 IV with just 2 levels), you don't care about the distribution for responses in the separate conditions. Rather, you focus on the distribution of the difference scores. In other words, in a repeated measures t-test, we're interested in change.
My questions are:
- Should I assess normality by looking at the 8 individual distributions associated with each conditions
- If yes, why is it different for a t-test (which is essentially calculated in the same way)
- If I shouldn't look at the 8 distributions mentioned above, what should I run my normality analysis on?
Best Answer
There is a reason that we talk about the normality 'assumption' rather than the normality 'condition'. Whether you are comfortable with the assumption of normality needs to come from knowledge about the science that generated the data, not the data itself.
The tests for normality, when used for justifying the normality assumption, will either give a meaningless answer to a meaningful question (small sample size) or a meaningful answer to a meaningless question (large sample size).
Plots of residuals from an appropriate model (including the repeated measures) can be used along with what you learn by doing your homework about where the data comes from to help you decide if you are comfortable with the normality assumption. But for deciding if the tests and intervals based on the normal are reasonable, dump the formal tests of normality.